We consider two dynamical models of increasing dimension: the
Lorenz-63 and the Lorenz-96 models, which are widely used
testbeds for filtering in chaotic dynamical systems.
The Lorenz-63 model is a three-dimensional system introduced
in [1]} that describes the natural convection of a heated
fluid. The state at time \(t\)  is a three-dimensional vector \(Z(t) = (Z_{1}(t),Z_{2}(t), Z_{3}(t))\)  whose dynamics are given
by the ODE system,
\( \frac{dZ_{1}}{dt} = -\sigma Z_{1} + \sigma Z_{2}, \;\;\; \frac{dZ_{2}}{dt} = - Z_{1} Z_{3} + \rho Z_{1} - Z_{2}, \;\;\; \frac{dZ_{3}}{dt} = Z_{1}Z_{2} - \beta Z_{3},\) 
